Hey all, were doing quadratics and completing the square and my teacher gave us about 30 problems to work on but I'm really stumped on half of them. Im going to list 3 problems that are similar in how they are setup, can you show me how to solve them? I think I can figure out how to do the rest then. 1,2 & 3 are all completing the square by the way! I know how to do quadratics without a problem.

#1. 2x2-x-6=0

#2. Y=-x2+4x-7

#3. 3m2+4m-15=0


And this one we needed to do in quadratic. I got all the way to the end but the last part confused me.

2w2+3w+3=0
Then I did: the brackets will mean square root box thing, and the --- means divide, I=imaginary #

-3 +/- [(3)2-4(2)(3)]

-3+/-[9-24]
-----------
4

-3+/-[-15]
----------
4
^--that’s what I got.

The book says the answer is:

-3+/-i[16]
----------
4

I understand where you get the “I” from, but why there is a 16 instead of 15 there is what has me confused.

Really appreciate the help

here... ill show you how to do the first one...

the only thing I'm going to do different is use the power sign for the exponent

where you wrote 2x2, ill write 2x^2 to emphasize the x is to the power of 2

so 2x^2 - x - 6 = 0

step one: move the term wout x to the other side

2x^2 - x = 6

step two: if the square term has a number in front, divide through by it. If there is no coefficient skip this step. Here there is a 2 in front of the x^2 so

(2x^2)/2 - (x/2) = 6/2 which is also x^2 - 1/2x = 3

step three: including the sign, take half of the coefficient in front of the x term, then square it. Here the x term is -1/2x, so take half of -1/2 = 1/2 * (-1/2) = -1/4... half of one half is one forth. Then square the result (-1/4)^2 = 1/16

step four: take the result you just got and add it to both sides.

so to x^2 - 1/2x = 3 you need to add 1/16 on each side =

x^2 - 1/2x + 1/16 = 3 + 1/16

which is the same on the right as 48/16 + 1/16 = 49/16

x^2 - 1/2x + 1/16 = 49/16

OK so far?

step five: then convert the left side to the square form. Remember the result we had when we took half of the x coefficient, including the sign? We'll use that here

(x-1/4)^2 = 49/16

does this make sense? We took half the term and squared it, added it to both sides, and then used that half of the term for the square form.

then you square root both sides... bracket will mean square root

[(x-1/4)^2 = [49/16 or x - 1/4 = +/- [49/16 or x - 1/4 = +/-7/4

so you have x - 1/4 = +/- 7/4

that should get you through the others as well...

you might want to write the steps down... you'll do them the same each time. Be careful about the sign in step five... when you looked at half of the x coefficient including sign... if you forget the sign the answer will be wrong.

ill try to look at the last problem tonight if I have time.

As for the last problem, I also got what you did...

Ended up with

(-3 +/- [-15) / 4

And [-15 is also I[15

So id say that the answer in the book is wrong. It happens.

Until someone else checks this and shows us our mistake, I got what you did.